Wing Foot is a shoe franchise commonly found in shopping centers across the Unit

Question

Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of choosing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 63% of all Wing Foot stores show a profit the first year, 73% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 86% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(A and B), if P(A) = 0.63, P(B) = 0.73, and P(B | A) = 0.86. Round your answer to the nearest hundredth.

Explanation / Answer

P(A) = 0.63

P(B) = 0.73

P(B|A) = 0.86

By multiplication theorem of probability

P(A and B) = P(A). P(B|A)

P(A and B) = 0.63 x 0.86 = 0.5418

P(A and B) = 0.5418

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